Abstract: Under the constraint of constant illumination, an information criterion is formulated for the Fisher information that compressed sensing measurements in optical and transmission electron microscopy contain about the underlying parameters. Since this approach requires prior knowledge of the signal's support in the sparse basis, we develop a heuristic quantity, the detective quantum efficiency (DQE), that tracks this information criterion well without this knowledge. In this paper, it is shown that for the investigated choice of sensing matrices, and in the absence of read-out noise, i.e., with only Poisson noise present, compressed sensing does not raise the amount of Fisher information in the recordings above that of Shannon sampling. Furthermore, enabled by the DQE's analytical tractability, the experimental designs are optimized by finding out the optimal fraction of on pixels as a function of dose and read-out noise. Finally, we introduce a regularization and demonstrate, through simulations and experiment, that it yields reconstructions attaining minimum mean squared error at experimental settings predicted by the DQE as optimal.

Abstract: An efficient model-based estimation algorithm is introduced to quantify the atomic column positions and intensities from atomic resolution (scanning) transmission electron microscopy ((S)TEM) images. This algorithm uses the least squares estimator on image segments containing individual columns fully accounting for overlap between neighbouring columns, enabling the analysis of a large field of view. For this algorithm, the accuracy and precision with which measurements for the atomic column positions and scattering cross-sections from annular dark field (ADF) STEM images can be estimated, has been investigated. The highest attainable precision is reached even for low dose images. Furthermore, the advantages of the model-based approach taking into account overlap between neighbouring columns are highlighted. This is done for the estimation of the distance between two neighbouring columns as a function of their distance and for the estimation of the scattering cross-section which is compared to the integrated intensity from a Voronoi cell. To provide end-users this well-established quantification method, a user friendly program, StatSTEM, is developed which is freely available under a GNU public license.

Abstract: The intensity levels in a three-dimensional (3D) reconstruction, obtained by electron tomography, can be influenced by several experimental imperfections. Such artifacts will hamper a quantitative interpretation of the results. In this paper, we will correct for artificial intensity variations by determining the 3D point spread function (PSF) of a tomographic reconstruction based on high angle annular dark field scanning transmission electron microscopy. The large tails of the PSF cause an underestimation of the intensity of smaller particles, which in turn hampers an accurate radius estimate. Here, the error introduced by the PSF is quantified and corrected a posteriori.

Abstract: Source size broadening is an important resolution limiting effect in modern STEM experiments. Here, we propose an alternative method to measure the source size broadening making use of a holographic biprism to create interference patterns in an empty Ronchigram. This allows us to measure the exact shape of the source size broadening with a much better sampling than previously possible. We find that the shape of the demagnified source deviates considerably from a Gaussian profile that is often assumed. We fit the profile with a linear combination of a Gaussian and a bivariate Cauchy distribution showing that even though the full width at half maximum is similar to previously reported measurements, the tails of the profile are considerable wider. This is of fundamental importance for quantitative comparison of STEM simulations with experiments as these tails make the image contrast dependent on the interatomic distance, an effect that cannot be reproduced by a single Gaussian profile of fixed width alone.

Abstract: The charge-coupled devices used in electron microscopy are coated with a scintillating crystal that gives rise to a severe modulation transfer function (MTF). Exact knowledge of the MTF is imperative for a good correspondence between image simulation and experiment. We present a practical method to measure the MTF above the Nyquist frequency from the beam blocker's shadow image. The image processing has been fully automated and the program is made public. The method is successfully tested on three cameras with various beam blocker shapes.

Abstract: Statistical parameter estimation theory is proposed as a method to quantify electron microscopy images. It aims at obtaining precise and accurate values for the unknown structure parameters including, for example, atomic column positions and types. In this theory, observations are purely considered as data planes, from which structure parameters have to be determined using a parametric model describing the images. The method enables us to measure positions of atomic columns with a precision of the order of a few picometers even though the resolution of the electron microscope is one or two orders of magnitude larger. Moreover, small differences in averaged atomic number, which cannot be distinguished visually, can be quantified using high-angle annular dark field scanning transmission electron microscopy images. Finally, it is shown how to optimize the experimental design so as to attain the highest precision. As an example, the optimization of the probe size for nanoparticle radius measurements is considered. It is also shown how to quantitatively balance signal-to-noise ratio and resolution by adjusting the probe size.

Abstract: It is not straightforward to determine resolution for a 3D reconstruction when performing an electron tomography experiment. Different contributions such as missing wedge and misalignment add up and often influence the final resolution in an anisotropic manner. The conventional resolution measures can not be used for all of the reconstruction techniques, especially for iterative techniques which are more commonly used for electron tomography in materials science. Here we define a quantitative resolution measure that determines the resolution in three orthogonal directions of the reconstruction. As an application we use this measure to determine the optimum number of simultaneous iterative reconstruction technique (SIRT) iterations to reconstruct the gold nanoparticles, based on a high angle annular dark field STEM (HAADF-STEM) tilt series.

Abstract: Depth sectioning in high angular annular dark field scanning transmission electron microscopy is considered a candidate for three-dimensional characterization on the atomic scale. However at present the depth resolution is still far from the atomic level, due to strong limitations in the opening angle of the beam. In this paper we introduce a new, parameter based tomographic reconstruction algorithm that allows to make maximal use of the prior knowledge about the constituent atom types and the microscope settings, so as to retrieve the atomic positions and push the resolution to the atomic level in all three dimensions.

Abstract: The 3D morphology and distribution of lenticular Ni4Ti3 precipitates in the austenitic B2 matrix of a binary Ni51Ti49 alloy has been investigated by a slice-and-view procedure in a dual-beam focused ion beam/scanning electron microscope system. Due to the weak contrast of the precipitates, proper imaging conditions need to be selected first to allow for semi-automated image treatment. Knowledgeable imaging is further needed to ensure that all variants of the precipitates are observed with equal probability, regardless of sample orientation. Finally, a volume ratio of 10.2% for the Ni4Ti3 precipitates could be calculated, summed over all variants, which yields a net composition of Ni50.27Ti49.73 for the matrix, leading to an increase of 125 degrees for the martensitic start temperature. Also, the expected relative orientation of the different variants of the precipitates could be confirmed.

Abstract: Ni4Ti3 precipitates play an important role in the shape memory and superelastic behaviour of thermo-mechanically treated Ni-Ti material. The 3D morphology and distribution of such precipitates with lenticular shape and rhombohedral atomic structure in the austenitic B2 matrix of a binary Ni-rich Ni-Ti alloy has been elucidated via a slice view procedure in a Dual-Beam FIB/SEM system. With the sequence of cross-section SE images obtained from the SEM, a 3D reconstruction has been achieved after proper alignment and image processing, from which both qualitative and quantitative analysis can be performed. Careful imaging is needed to ensure that all variants of the precipitates are observed with equal probability, regardless sample orientation. Moreover, due to the weak contrast of the precipitates, proper imaging conditions need to be selected to allow for semi-automated image treatment. Finally, a volume ratio of 10.2% for the Ni4Ti3 precipitates could be calculated, summed over all variants, which yields a net composition of Ni50.36Ti49.64 for the matrix, leading to an increase of 113 degrees for the martensitic start temperature Ms. Also, the expected relative orientation of the different variants of the precipitates could be confirmed. In the near future, other quantitative measures on the distribution of the precipitates can be expected.